Problem: The sum of two numbers is $169$, and their difference is $27$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 169}$ ${x-y = 27}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 196 $ $ x = \dfrac{196}{2} $ ${x = 98}$ Now that you know ${x = 98}$ , plug it back into $ {x+y = 169}$ to find $y$ ${(98)}{ + y = 169}$ ${y = 71}$ You can also plug ${x = 98}$ into $ {x-y = 27}$ and get the same answer for $y$ ${(98)}{ - y = 27}$ ${y = 71}$ Therefore, the larger number is $98$, and the smaller number is $71$.